MARS IN THE AUTUMN OF 1877. 
243- 
47° 56' (the angle n of the formulas), and draw dT square 
to ab. From da measure off the arc dap'bf equal to the 
right ascension of Mars at the time considered. (I have 
taken the actual right ascension at the time of opposition 
on September 5, viz. 347° 19'; otherwise, for the general 
illustration of the method, I should have selected a more con- 
venient arc.) From b measure off an arc on bpap' equal to 
the northerly declination of the planet : —the declination being 
southerly on Sept. 5 — the extremity of this arc will fall on bp' 
as at h, where bh is an arc of 12° 9-J'. Draw the ordinates fm, 
hm intersecting in M, corresponding to the place of Mars on 
the star-sphere, where pop' is the polar axis and aob the projec- 
tion of the celestial equator, y lying on the concavity of the 
sphere thus projected. Now take arc pp = 39° 42', the inclina- 
tion of the polar axis of Mars to the earth’s polar axis (No. 1 
of the formulas), and draw the diameter pop'. Then, if the 
point m be supposed brought to the centre o by two rotations, 
one round pop', the other round ab, the position taken up by 
pp' will be the true projection of the polar axis of Mars at the 
time considered. The construction for this purpose is indicated 
by the dotted lines in the figure. (The full lines indicate con- 
structions common to all cases ; the broken lines indicate con- 
structions for finding M ; the heavy lines indicate final result,, 
the broken heavy line being that part of the polar axis of Mars- 
which lies between his centre and his unseen pole). Draw hk 
square to op', with centre K describe arc hl, meeting fm; 
draw pk square to op, describe quadrant plh about /&, take arc 
hi — hl (i.c. angle hkl = angle hkl); and draw lp x square to pl\. 
Then p Y is the position of p after first rotation. Next, drawing 
ap Y n square to ob, let p l b square to an meet arc ah'b about 
n as centre in b ; take arc bh' = bh ; then h'p 2 square to cm 
gives the place of p after second rotation. Thus p<f>p\ is the 
position of the axis of Mars. It is readily seen that p 2 cor- 
responds to the unseen pole, p\ to the visible pole. We must 
now take oe on op 2 equal to ok, then e is the place where the 
equator crosses the central meridian. The rest of the construc- 
tion is the ordinary projection of a sphere. Half the equator 
is shown. It is a good plan, by the way, to complete the 
construction for one-half only on tracing paper, and to prick 
off the two halves in the final drawing from the same tracing, 
first from one side, then from the other. This secures sym- 
metry with respect to the polar axis. 
The construction above given occupies only a few minutes in 
practice, and gives results quite accurate enough for the correc- 
tion of the position of Mars’s polar axis. In fact it would be 
well indeed if the telescopic observers could obtain results even 
nearly as accurate as such constructions afford. 
